I've used clipless for everything for more than 30 years so I have no idea how flat pedals feel but I don't know if they would help you. I have done long, climbing mountain bike rides with a guy who used flats and 1 of the women I ride off road with also uses flats and they both seem to do fine.
I can't think of anyone I've ridden with using flats on the road. I'm sure the people who drop me would still drop me if they switched to flats.
Clipless might help with your spin. I can't swear to the pulling up thing. I mean, I think I do it but lots of forum experts say it doesn't work. You might just have to try clipless. I recommend mtb style if you do.